Proc. of 38 th Scandinavian Symposium on Physical Acoustics, Geilo, Norway, February 1-4, 2015 Volume backscattering of finite-amplitude acoustic waves: Power flow, sampled volume, and scattering cross section Per Lunde a,b University of Bergen, Dept. of Physics and Technology, P.O.Box 7803, N-5020 Bergen, Norway Audun O. Pedersen c Christian Michelsen Research AS, P.O.Box 6031, Postterminalen, N-5892 Bergen, Norway ABSTRACT In multiple-target volume backscattering applications, the volume and cross-sectional area interrogated by the acoustic beam may be in- fluenced by finite-amplitude sound propagation effects. To analyze the magnitude of such effects, generic governing equations for propagation and backscattering of small- and finite-amplitude signals in fluid media are formulated in terms of power budget equations, describing transmit- receive electrical power transfer functions, applicable to single-target and volume backscattering. Effective sampled area and sampled volume of the volume backscattering system are defined, accounting for two-way sound propagation and the transmit and receive properties of the transducer. Volume backscattering power flow is interpreted in terms of the equivalent backscattering cross section of the sampled volume. Expressions are given which describe how the sampled area, the sampled volume, and the backscattering cross-section of the sampled volume, are influenced by finite amplitude effects. a) Corresponding author. Electronic mail: per.lunde@ift.uib.no b) Also with Christian Michelsen Research AS, P.O.Box 6031, Postterminalen, N-5892 Bergen, Norway; and the Michelsen Centre for In- dustrial Measurement Science and Technology, Norway. c) Present address: ClampOn AS, Vaagsgaten 10, N-5160 Laksevaag, Bergen, Norway. I. INTRODUCTION Acoustic backscattering is used in diverse applications, such as remote sensing, acoustic Doppler current profiling, fish abundance estimation, fish species identification, acoustic imaging, etc. Control with the volume and cross-sectional area being interrogated by the sound field, is important. At long measurement ranges, or in noisy environment, challenges with low or marginal signal-to-noise ratio (SNR) may be experienced. In such situations, manufactures or us- ers may be tempted to increase the electrical transmit power of the equipment. The resulting high sound pressure levels may introduce finite-amplitude effects as the sound signal propa- gates through the fluid medium. The chance of introducing finite-amplitude sound propagation effects increase with in- creasing frequency [1]. The volume and cross-sectional area interrogated by the acoustic beam (here referred to as the “sampled volume” and “sampled area”, respectively) are affected when finite- amplitude effects are present. The reason for that is the pres- sure dependency of the sound velocity in fluids [1]. The high and low pressure portions of the sound signal travel with dif- ferent sound speeds, causing signal distortion. During propa- gation through the fluid medium, energy is transferred from the signal’s fundamental frequency component to the higher harmonic components. Consequently, for applications in which the fundamental frequency is the component exploited, the properties of the interrogating sound field are altered. The sound pressure is highest at the main lobe. The fundamental frequency component’s loss of energy is thus largest there, causing changed spatial distribution of the inter- rogating sound field, such as flattened beam pattern and in- creased beam width [1-4]. The altered beam pattern leads to changed sampled volume and area. If not aware of or controlling such influences, a user may easily (and erroneously) assume that a different portion of the fluid volume is interrogated, than what is actually the sit- uation. In applications of volume backscattering at high signal amplitudes, it is thus of interest to control and quantify how large the possible effects of finite amplitude are, such as with respect to changed sampled area and volume. The influence of range, frequency, and electrical transmit power is essential. Current literature appears to be sparse on expressions describ- ing the effects of finite amplitude on the volume and cross- sectional area being interrogated by the sound beam in volume backscattering applications. The objective of the present work is to improve on this lack of knowledge by giving expressions which describe how the sampled area, the sampled volume, and the backscattering cross-section of the sampled volume, are influenced by finite amplitude effects. II. ANALYSIS A monostatic measurement situation with single-target and multiple-target (volume) backscattering is considered. Generic governing equations for propagation and backscatter- ing of small- and finite-amplitude signals in fluid media are formulated in terms of power budget equations [5]. That is, in